Use the rule for order of operations to simplify the expression as much as possible: \( 4+2(8-2)-7=\square \)

To simplify the expression \( 4+2(8-2)-7 \), we start by following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). First, we solve the parentheses: \[ 8-2 = 6 \] Next, we replace the parentheses in the expression: \[ 4 + 2(6) - 7 \] Now, we perform the multiplication: \[ 2(6) = 12 \] The expression now looks like this: \[ 4 + 12 - 7 \] Next, we proceed with the addition: \[ 4 + 12 = 16 \] Finally, we perform the subtraction: \[ 16 - 7 = 9 \] So, the simplified expression equals \( 9 \). Therefore, \[ 4+2(8-2)-7=\boxed{9} \]